Thin sheets, called tapes, that are used in manufacturing oxygen membranes, capacitors, etc., are formed by squeegeeing a slurry into a thin film, allowing the film to dry to a rubbery condition, and then baking the film in an oven wherein it shrinks and achieves a brittle consistency. During baking, the film must be held down against a flat or other surface to which the final sheet is to conform, to avoid curling of the sheet into a brittle unwanted shape. A vacuum hold-down can be used to hold the sheet while it is baked. However, it is found that the sheet is subject to cracking as it shrinks, due to the vacuum holding all portions of the original sheet in their original positions. A device for holding thin workpieces against a surface, which enabled the workpieces to change dimensions while they continued to be held closely against the surface, would be of value in the forming of the sheets described above as well as other thin workpieces that had to be heat treated.